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For which L(s) will be these vectors linearly dependent?

  1. Oct 24, 2011 #1
    So i have 3 vectors:
    a= [1 1 1]
    b= [2 L 0]
    c= [L 2 3]

    How do I calculate the L in order to make these vecotrs linearly dependent?

    How does ß depend from L if v= [ß 0 -1] and v is in span(a b c)?

    Thank you!
     
  2. jcsd
  3. Oct 24, 2011 #2

    HallsofIvy

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    Do you know what "linearly dependent" means? Use the definition of "linearly dependent" You will get a cubic equation for L but, fortunately, there's 1 obvious root.

    For the second question, are we to assume that L is one of those values? Otherwise, the span of a, b, and c is all of R3 and [itex]\beta[/itex] can be anything.
     
  4. Oct 24, 2011 #3
    I guess I know.

    I wrote 3 equations:

    α + 2β + Lγ = 0
    α + Lβ + 2γ = 0
    α + + 3γ = 0

    And i got, L can be 1 or 2. Then I checked it and for these Ls the vectors are dependents. But how do I know that there aren't more Ls.

    For the second question. Yes L is from those values.
     
  5. Oct 24, 2011 #4
    But I maybe got the definition wrong.
     
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